Document Type : Research Paper

Authors

• Taher kouchaki tajani ¹
• Ali Mohtashami ²
• maghsoud Amiri ³
• Reza Ehtesham Rasi ⁴

¹ Ph.D. in Industrial Management, Faculty of Management and Accounting, Qazvin Branch, Islamic Azad University, Qazvin, Iran

² Associate Professor of Department of Industrial Management,Faculty of Management and Accounting, Qazvin Branch, Islamic Azad University, Qazvin, Iran

³ Professor, Department of Industrial Management,Faculty of Management and Accounting, Allameh Tabataba'i University, Tehran, Iran

⁴ Assistant Professor of Department of Industrial Management,Faculty of Management and Accounting, Qazvin Branch, Islamic Azad University, Qazvin, Iran

Abstract

In this paper, we have proposed a model based on Mixed Integer Non-Linear Programming for the blood supply chain under conditions of uncertainty in supply and demand, from the stage of receiving blood from volunteers to the moment of distribution in demand centers. The challenges addressed in this optimization model are the reduction of blood supply chain costs along with minimizing the shortage and expiration rate of blood products. The Markov chain has been used to address the uncertainty of donor blood supply. To estimate the needs of medical centers, the received demand is considered fuzzy. Then, the proposed model is solved in small dimensions by GAMS software and in large dimensions by Bat and Whale meta-heuristic algorithms, and the results are presented. In addition, a case study is presented to show the applicability of the proposed model. The results show a reduction in the level of costs as well as a reduction in the shortage and expiration of blood products in the supply chain.
Introduction
One of the important topics researched in the global healthcare systems of different countries is the improvement of supply chain performance. The health system has one of the most complex and challenging supply chains due to its direct relationship with human lives. Issues such as uncertainty in blood demand and supply, blood inventory planning, delivery schedule, ordering time, attention to expiration date, and limited human resources are among the challenging issues in the field of health, especially the supply chain of blood and blood products. A unit of blood, from the time it is received from the donor to the time it is injected into the patient as whole blood or blood product, includes many processes and challenges that must be taken into account to ensure the health of the blood and the health of the supply chain. Redesigning an existing blood supply chain is not possible in the short term due to significant costs and time required, so using existing facilities and optimizing conditions is more preferable than reestablishing equipment, blood centers, and other facilities related to the blood supply chain. In this research, by presenting a mathematical model, we try to optimize the tools and facilities in a blood supply chain. The important goal in the blood supply chain is the cost factor. The costs incurred on the blood supply chain include costs such as blood collection from volunteers, product processing and blood inventory costs in hospitals and blood centers, and blood transfer costs to demand centers. On the other hand, the balance in storage and waste reduction is also very important in this chain. High storage increases the amount of inventory (increase in cost) and also increases the rate of perishability (increase in cost) of blood products. It is important to pay attention to the fact that the reduction of costs should be accompanied by the reduction of shortages and waste. In addition to the lack of blood, improper distribution and untimely supply of blood to hospitals can be completely disastrous. Requests to blood centers are made under certain conditions, such that the requested product(s) are separated in terms of blood group or the presence or absence of a specific antigen. Paying attention to blood groups and compatibility indicators is one of the principles of blood transfusion, and not observing them can cause unfortunate events.
Due to the disproportionate percentage of distribution of blood groups among volunteers, there has always been a possibility of a shortage in the supply chain. In the medical world, in case of a shortage of a blood product of a certain group, attempts are made to replace that product from groups that can be matched. This will reduce the shortage and save the lives of patients whose blood with the required blood group and RH is not available at the same moment. In order to solve this challenge, in the upcoming research, a solution based on the versatility of unanswered demands will be considered, which will be included in the mathematical model. Another important issue is the age of the demand for the requested product, which creates an age-based demand in the supply chain. (Some special patients need fresh or normal products according to the type of disease.)
Methodology
In this research, a comprehensive mathematical model has been developed in the form of a MINLP model. The research model is based on a comprehensive blood supply chain consisting of three components: collection, processing, and consumption of blood products. There are three types of collection centers in this model: first, vehicles that serve blood donors at predetermined locations and collect blood; second, fixed collection facilities located in some areas of the city that solely perform the task of collecting blood; and third, blood centers (blood transfusion centers) that perform both blood collection work and other tasks related to product processing, testing, and transfer planning to demand centers and hospitals. The next part of the model is related to the processing of the collected blood. In this part, the blood collected by the collectors in the blood center is aggregated, the percentage of each blood group is determined, and according to the need in the blood centers, products such as red blood cells, platelets, and whole blood plasma are sent to hospitals. It is worth noting that as blood is converted into other products, some characteristics of the product, including the age of the products, differ from each other. Therefore, in the continuation of transferring the products and responding to their demand, the age of the blood product will be considered. Additionally, it should be noted that the blood product requested from the demand centers is in two forms. For some special patients and in special surgeries, a series of blood products with a certain age (young blood) are needed. Therefore, the importance of the age of the blood sent to the hospitals is also seen in the model. In the real world, in the face of a shortage in hospitals, a solution is thought out, which is to use the principle of adaptability of blood groups. Through a pre-accepted adaptability matrix, a series of demands for blood groups g, in case of shortage, can be satisfied with the supply of blood groups f turn around. Deterministic supply chain network design models do not take into account the uncertainties and information related to the future affecting the supply chain parameters and as a result cannot guarantee the future performance of the supply chain because due to the inherent and fluctuating and sometimes severe change in the environment of many operating systems Parameters in optimization problems have random and non-deterministic characteristics. In this research, two different approaches have been used to face the uncertainty in blood supply and demand values. For the demand, a triangular fuzzy approach has been proposed. According to the conditions of uncertainty, the appropriate alpha cut is selected based on the opinion of the decision-makers, and the demand is adapted to the conditions. Regarding the amount of supply, in order to estimate the number of donors in future periods, we have used the Markov chain to predict the number of donors based on the records in the past.
Findings
In order to evaluate the presented model, it is necessary to solve the research in both small and large sizes to determine the reaction of the research target function to changes in the parameters of the problem. For this purpose, the research model was first coded in GAMS 24.1 software. According to the designed sample problems, up to a certain size, it is possible to solve the problem within a certain time frame using GAMS software. However, as the size of the problem increases and the time to reach the answer also increases, meta-heuristic algorithms such as WOA and BAT were employed to solve this problem. The results indicate that the Whale Optimization Algorithm (WOA) performed better. Subsequently, based on a case study, a problem was presented to illustrate the efficiency of the model and its solution method. The results obtained for the objective function and the values obtained for the main variables of the research demonstrate the effectiveness of the model and its solution approach.
Conclusion
The purpose of this article is to design a comprehensive supply chain that includes three parts: collection, processing, and distribution of blood products. The supply chain comprises mobile and fixed blood collection units that receive blood from donors and send it to blood centers. At these centers, blood is processed into required products and then distributed to demand centers based on demands categorized as fresh or normal products. In this research, the objective was to minimize costs such as blood collection, blood inventory in blood centers and hospitals, as well as the cost of blood products expiring due to non-use. To address blood deficiency, the blood compatibility system was incorporated into the model. This system ensures that if a certain product of a certain group is not available, a compatible product from another group is sent as a replacement. The model was solved using the exact solution approach of GAMS software for smaller-sized problems. However, for larger-sized problems, meta-heuristic algorithms such as WOA and BAT were employed to achieve reasonable solving times. Additionally, a fuzzy coefficient was proposed for relatively accurate demand prediction, and the Markov chain and the Kolmograph left-hand theorem were utilized to predict the number of blood donors. The results obtained from small-sized problems using accurate solver algorithms, as well as medium and large-sized problems using WOA and BAT meta-heuristic algorithms, demonstrate the efficiency of the designed model. Finally, a sensitivity analysis based on changes in fuzzy coefficients of demand and coefficients, including the alpha cut transformation function, and its effect on the objective function are presented.

Keywords

• Blood supply chain
• Markov chain
• mixed integer Non-linear programming
• Whale Metaheuristic algorithm
• Bat Metaheuristic algorithm